ON HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 



329 



The negative sign prefixed to the minimum current indicates that the current 

 turns in the clockwise direction. 



Harmonic Analysis of Hourly Heights. 



6. We assume that the height of the water at any station may be expressed as 

 the sum of a number of Fourier's series in time. In each of these series only a few 

 terms are important ; for instance, in the largest (M) series, the important terms 

 are the constituents 



M„ Mj, M„ M<, U„ Mg, 



while in others {e.g. N or O) there is only one important term (N, or 0,). 



A typical short period series will have speeds 



<r,_ 2(rr, 3<r^, .... mo-,, . . . 



where o-^ is that of the diurnal constituent. We shall take r = for the principal 

 solar series, so that 2ir/<ro is a mean solar day. 



The data for analysis consist in a number of heights at intervals of time equal 

 to one mean solar hour. 



The Isolation of the Principal Solar Series. 

 Arithmetic means are taken of the heights at the times 



h_2ir 



,r (,.h\ 2t /o . *\ 2t /n - 1 +i'\ ?? 



for each of the values 0, 1,2, . . . . 23 of A. 



For any value of h this process will leave unchanged the term 



R cos (mffj, — e) . 



and consequently the whole S series. 

 From the term 



B cos (nffrt — f) . 



however, it will give 



R 



N 



N -1 



2 cos 



H-^Js 



which is equal to 



|-^2cos(2«[«(^-l) + 24 ^]'-*(' 



(1) 



(2) 

 (3) 

 (4) 



(6) 



